Making the buttonpress F6 into a scripted button
If you mean the "redo last" operation, which I believe is the default key binding for this function, then you can use this: (note that    you'll have to include bl_info and register and unregister functions    as in the code snippet below )

import bpy

class redo_last_operator(bpy.types.Operator):
    bl_idname = "screen.redo_last_operator"
    bl_label = "redo last"
    bl_options = {'REGISTER', 'UNDO'}

    def execute(self,context):
        bpy.ops.screen.redo_last()
        return {'FINISHED'}


Please note that importing this as an add-on will only add the operator to Blender, not add a Button to any panel. You can do that yourself, however, by creating a panel for it or adding it to a Panel yourself. The following code will create a panel as well:

import bpy

bl_info = {
    "version": (1, 0),
    "blender": (2, 75, 0),
    "name": "Redo Last Operator",
    "description": """Creates an operator for the redo last menu""" ,
    "category": "File",
    "location": """""",
}

class redo_last_operator(bpy.types.Operator):
    # this class is meant only for destroying data blocks of a certain type, very powerful but very dangerous
    bl_idname = "screen.redo_last_operator"
    bl_label = "redo last"
    bl_options = {'REGISTER', 'UNDO'}

    def execute(self,context):
        bpy.ops.screen.redo_last()
        return {'FINISHED'}

class redo_last_operator_panel(bpy.types.Panel):
    bl_label="redo last"
    bl_idname="redo_last_operator"
    bl_space_type = "VIEW_3D"
    bl_region_type = "TOOLS"
    bl_category='Addons'

    def draw(self,context):
        self.layout.operator(redo_last_operator.bl_idname)

def register():
    bpy.utils.register_class(redo_last_operator)
    bpy.utils.register_class(redo_last_operator_panel)

def unregister():
    bpy.utils.unregister_class(redo_last_operator)
    bpy.utils.unregister_class(redo_last_operator_panel)

if __name__ == "__main__":
    register()


If, on the other hand, you meant another operation, you can use the same code and still bind it to the button by replacing the code under execute().